Argentina completed the turnaround from the shock opening World Cup loss to Saudi Arabia by qualifying for the last 16 in impressive style against Poland - who went through on goal difference having finished level on points with Mexico.
Lionel Messi was the catalyst for the crucial win against Mexico that got Argentina's campaign back on track, and he was instrumental again as they illustrated why they were regarded as one of the tournament favourites to set up a second-round match against Australia.
Poland were set to progress by virtue of the Fifa Fair Play rule for having fewer yellow cards than Mexico - until Saudi Arabia pulled one back deep into stoppage time in their 2-1 loss to the Concacaf side. The Poles will now face France after surviving an incredibly dramatic finale in which another goal for Argentina or Mexico would have knocked them out.
Argentina ran out comfortable winners with second-half goals from Brighton's Alexis Mac Allister and Manchester City striker Julian Alvarez, but the game still held real drama and jeopardy in the closing stages as Poland knew another goal conceded, or another goal for Mexico against the Saudis, would send them out on goal difference.
Argentina dominated throughout but had to wait until after the second half to make the breakthrough as Messi had a first-half penalty saved by Poland keeper Wojciech Szczesny after the pair collided in an aerial challenge, a harsh award after a video assistant referee consultation.
Mac Allister gave Argentina the lead they deserved when he swept home Nahuel Molina's cross a minute after the break and Alvarez sealed victory with a fine finish into the top corner in the 67th minute.
Impressive Argentina show class
Argentina's improvement continued as they produced their best performance of the World Cup to outclass a disappointing Poland.
The Argentines shook off the shock of that stunning loss to Saudi Arabia to settle their nerves with a Messi-inspired win against Mexico then stepped up to another level to confirm a last-16 game against Australia.
Messi's first-half penalty miss was a minor interruption on their path to victory as they held complete command of territory and possession against a passive Poland, especially given what was at stake.
Argentina keeper Emi Martinez did not have a moment of anxiety and once Mac Allister put them ahead the game was virtually over, Alvarez confirming it with a superb strike past the excellent Szczesny that hinted at his own rich potential.
Messi showed flashes of his mercurial best but this was a complete performance from Argentina who played with greater intensity and fire than they have so far.
They have taken their time to show why they are so highly regarded but produced plenty of evidence here to illustrate just how dangerous they will be in the knockout stage.
Passive Poland ride their luck
It was symbolic of this lacklustre Poland performance that their greatest show of passion all night came after the game had finished when they punched the air as news of Saudi Arabia's goal against Mexico that confirmed their place in the last 16 filtered down on to the pitch.
Poland's players revelled in the good tidings as they waved red and white flags on the pitch, barely able to believe they were through to face France.
They can consider themselves fortunate to be there after this poor performance in which they never troubled Argentina and the great striker Robert Lewandowski did not receive any service worthy of the name.
One exception to the mediocre fare from the rest of his colleagues was former Arsenal goalkeeper Szczesny, who was magnificent throughout, saving Messi's penalty and producing other stops in a faultless display.
Poland are through and enjoyed their celebration but they will have to step up several levels to trouble France.
Player of the match
Mac AllisterAlexis Mac Allister
Poland
Squad number1Player nameSzczesny
Squad number2Player nameCash
Squad number9Player nameLewandowski
Squad number15Player nameGlik
Squad number20Player nameZielinski
Squad number18Player nameBereszynski
Squad number6Player nameBielik
Squad number14Player nameKiwior
Squad number10Player nameKrychowiak
Squad number16Player nameSwiderski
Squad number24Player nameFrankowski
Squad number8Player nameSzymanski
Squad number13Player nameKaminski
Squad number26Player nameSkóras
Squad number3Player nameJedrzejczyk
Squad number23Player namePiatek
Argentina
Squad number20Player nameMac Allister
Squad number10Player nameMessi
Squad number9Player nameÁlvarez
Squad number23Player nameMartínez
Squad number11Player nameDi María
Squad number24Player nameFernández
Squad number7Player nameDe Paul
Squad number13Player nameRomero
Squad number26Player nameMolina
Squad number19Player nameOtamendi
Squad number8Player nameAcuña
Squad number3Player nameTagliafico
Squad number5Player nameParedes
Squad number16Player nameAlmada
Squad number6Player namePezzella
Squad number22Player nameMartínez
Line-ups
Poland
Formation 4-4-2
1Szczesny
2Cash15Glik14Kiwior18Bereszynski
20Zielinski6Bielik10Krychowiak24Frankowski
9Lewandowski16Swiderski
1Szczesny2Cash15Glik14Kiwior18BereszynskiSubstituted forJedrzejczykat 72'minutes20Zielinski6BielikSubstituted forSzymanskiat 62'minutes10KrychowiakBooked at 78minsSubstituted forPiatekat 83'minutes24FrankowskiSubstituted forKaminskiat 45'minutes9Lewandowski16SwiderskiSubstituted forSkórasat 45'minutesSubstitutes
3Jedrzejczyk4Wieteska5Bednarek7Milik8Szymanski11Grosicki12Skorupski13Kaminski17Zurkowski19Szymanski21Zalewski22Grabara23Piatek25Gumny26SkórasArgentina
Formation 4-3-3
23Martínez
26Molina13Romero19Otamendi8Acuña
7De Paul24Fernández20Mac Allister
11Di María10Messi9Álvarez
23Martínez26Molina13Romero19Otamendi8AcuñaBooked at 49minsSubstituted forTagliaficoat 59'minutes7De Paul24FernándezSubstituted forPezzellaat 79'minutes20Mac AllisterSubstituted forAlmadaat 84'minutes11Di MaríaSubstituted forParedesat 59'minutes10Messi9ÁlvarezSubstituted forMartínezat 79'minutesSubstitutes
1Armani2Foyth3Tagliafico4Montiel5Paredes6Pezzella12Rulli14Palacios15Correa16Almada17Gómez Villaverde18Rodríguez21Dybala22Martínez25MartínezReferee:Danny MakkelieAttendance:44,089Live Text
Match ends, Poland 0, Argentina 2.
Second Half ends, Poland 0, Argentina 2.
Lionel Messi (Argentina) wins a free kick in the attacking half.
Foul by Robert Lewandowski (Poland).
Corner, Argentina. Conceded by Kamil Glik.
Attempt blocked. Nicolás Tagliafico (Argentina) left footed shot from the centre of the box is blocked. Assisted by Thiago Almada.
Foul by Rodrigo De Paul (Argentina).
Piotr Zielinski (Poland) wins a free kick in the defensive half.
Attempt missed. Lautaro Martínez (Argentina) right footed shot from the right side of the box misses to the left.
Foul by Leandro Paredes (Argentina).
Michal Skóras (Poland) wins a free kick in the defensive half.
Substitution, Argentina. Thiago Almada replaces Alexis Mac Allister.
Substitution, Poland. Krzysztof Piatek replaces Grzegorz Krychowiak.
Substitution, Argentina. Lautaro Martínez replaces Julián Álvarez.
Substitution, Argentina. Germán Pezzella replaces Enzo Fernández.
Grzegorz Krychowiak (Poland) is shown the yellow card for a bad foul.
Alexis Mac Allister (Argentina) wins a free kick in the defensive half.
Foul by Grzegorz Krychowiak (Poland).
Attempt missed. Julián Álvarez (Argentina) right footed shot from the right side of the box is close, but misses to the right. Assisted by Lionel Messi with a through ball.
Substitution, Poland. Artur Jedrzejczyk replaces Bartosz Bereszynski.
Get the latest results and goal notifications for any team at the Fifa World Cup by downloading the BBC Sport app: Appleexternal-link - Androidexternal-link - Amazonexternal-link
Get your daily dose of Fifa World Cup reaction, debate & analysis with World Cup Daily on BBC Sounds